| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 107 === We investigate the terminal velocity and coupling distance of a free falling cylinder in viscous and incompressible flow, with the help of software simulator based on the immersed boundary method from previous work. We analyze the influence different physical parameters (Ex. density ratio, channel width, Archimedes number) have on terminal velocity and try to integrate an empirical equation of terminal velocity. We also observe the relation between coupling distance and above mentioned physical parameters in a simulation where the cylinder approaches the floor at terminal velocity, and integrate its empirical equation.
From these simulations, we observe that the relation between terminal velocity and density ratio remains similar to the analytical solution, even in a situation previously thought unfit for the analytical solution (at a higher Reynolds number.) We also observe that the terminal velocity and the Architecture number almost have a perfect linear relationship. The fitted empirical equation of terminal velocity has a root-mean-square error of 3.9%.
Regarding coupling distance, we can observe from the log-log graphs that density ratio and Architecture number have the same linear relationship with coupling distance. More importantly, we find that coupling distance increases with channel width, which induces the positive correlation between terminal velocity and coupling distance. The fitted empirical equation of coupling distance has a root-mean-square error of 8.9%.
At last, we combine the empirical equations to analyze the relation between Stokes number and coupling distance.
|
|---|
